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C₂×#6090 #88051

order	416
isoclinism	isoclinic class of D₁₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆ · Schur multiplier (H₂) = C₂

Aliases

Splittings

C₁₃ ⋊ C₂×C₁₆

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₈	D₁₃
commutator, hypocenter	C₁₃	C₂×C₁₆
Frattini	C₈	C₂×D₁₃
Fitting	C₂×C₈×C₁₃	C₂
socle, prime radical	C₂²×C₁₃	C₈
cosocle	C₈×C₁₃	C₂²
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₈

28 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 416

A minimal faithful permutation representation — 2 generators on 31 points:

(1,2)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17,18,21,19,22,24,27,20,23,25,28,26,29,30,31);(1,2)(3,4,6,8,10,12,14,15,13,11,9,7,5)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₄×#6090, #11718053, C₄⋊#6090, …
maximal normal subgroup of	C₄×#6090, #11718053, C₄⋊#6090, …
maximal quotient of	C₄×#6090, C₄⋊#6090, C₂×#88034, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(416, 18);